Brightness enhancement films such as Vikuiti™ film available from 3M Company, St. Paul, Minn. are transparent optical films that increase display (typically, liquid crystal display—LCD) brightness through improved light management. FIG. 1 schematically depicts the operation of a typical brightness enhancement film. The “inward” and “outward” directions are indicated by double-headed arrow Z. A plane surface 10 (often the outward viewing surface of a so-called light box 11 which observer V looks at through an angular range of viewing directions Y) emits light rays 12, 14, 16, 18, etc. diffusely (that is, with a so-called Lambertian distribution) such that the apparent luminance of surface 10 is the same from all viewing directions. Surface 10 has high diffuse reflectance, such that light box 11 has a high surface reflectance RS. In some circumstances, RS can be very close to 1.0, which is the theoretical maximum (but, in practice, unattainable) reflectance value. For example, a light guide of the type typically used to illuminate the LCD display of a laptop type computer can have very high reflectance. The following discussion assumes that RS is 1.0, but can easily be generalized to lower values of RS, in a manner well know to persons skilled in the art.
As shown in FIG. 1, a non-light absorbing prior art optical film 20 having a microstructured surface (e.g. bearing a large plurality of microreplicated prismatic structures) is placed adjacent and substantially parallel to the light-emitting plane of surface 10. As long as it is possible for some light to pass through film 20, then all light which passes from surface 10 to film 20 is eventually emitted through film 20. This is because no light is absorbed by film 20—any light incident upon film 20's inward surface that is not transmitted through film 20 is reflected by film 20 back toward surface 10. Such reflected light is again reflected, diffusely, by surface 10's light-emitting plane, a fraction of this twice-reflected light is transmitted through film 20, and the remainder is reflected by film 20 back toward surface 10, and so on ad infinitum. The intensity of the transmitted light can be described by a geometric series of the form:
                              T          T                =                                            (                              1                -                                  R                  d                                            )                        ⁢                          (                              1                +                                  R                  d                                +                                  R                  d                  2                                +                                  R                  d                  3                                +                …                            ⁢                                                          )                                =                                                    1                -                                  R                  d                                                            1                -                                  R                  d                                                      =            1                                              (        1        )            where Rd is the reflectance of film 20 to diffuse light. A more intuitive way to describe the situation is that since the light cannot be absorbed by film 20 or by light-emitting surface 10, it is all eventually emitted.
However, with film 20 in place, observer V does not necessarily perceive a display incorporating surface 10 and film 20 as having the same luminance when viewed from different ones of angular viewing directions Y. For example, a microstructured surface film 20 having an essentially transmissive appearance when viewed from a roughly normal (i.e. perpendicular) viewing direction, may have an essentially reflective appearance when viewed at steeper viewing angles. Clearly the spatially averaged luminance of the display, as perceived by the observer, must be lower at such steep angles. Since the total amount of light is the same, regardless of the range of angles over which the light is transmitted, it follows that the spatially averaged luminance of the display is higher when surface 10 is viewed from the normal direction.
If Rd is the reflectance of film 20 to diffuse (Lambertian) light as above, and if Tn is the transmittance of film 20 when viewed in an intended normal (i.e. perpendicular) viewing direction from the intended backlit (i.e. inward) side of film 20, then the relative brightness gain, Gn, in the normal viewing direction is:
                              G          n                =                              T            n                                1            -                          R              d                                                          (        2        )            Gn can be optimized by making film 20 as reflective as possible, without diminishing film 20's ability to transmit light in the normal viewing direction. For example, some Vikuiti™ brightness enhancement films available from 3M Company have a transmittance value Tn≈0.9 and a reflectance value Rd≈0.5, implying a theoretical maximum gain value of Gn≈1.8. In practice, the reflectance of light box 11's light emitting surface is less than 1.0, so this theoretical maximum gain value cannot be attained in practice, but it is a useful metric for comparison purposes.
Another desirable characteristic for a brightness enhancement film is a smooth variation of the light transmittance characteristic T as a function of viewing angle, since in many circumstances there will be a wide range of viewing angles, e.g. the preferred 0° (normal incidence) to 40° angular viewing range. Some prior art brightness enhancement films exhibit a very sharp transition between ranges of viewing directions having very high light transmissivity and ranges of viewing directions having very low light transmissivity. It is often necessary to add one or more light diffusers to the display to minimize this problem. This invention addresses the problem in a manner which increases the brightness of an LCD type display while providing a smooth variation in luminance as a function of viewing angle.